Deciphering a novel image cipher based on mixed transformed Logistic maps

Since John von Neumann suggested utilizing Logistic map as a random number generator in 1947, a great number of encryption schemes based on Logistic map and/or its variants have been proposed. This paper re-evaluates the security of an image cipher based on transformed logistic maps and proves that the image cipher can be deciphered efficiently under two different conditions: 1) two pairs of known plain-images and the corresponding cipher-images with computational complexity of $O(2^{18}+L)$; 2) two pairs of chosen plain-images and the corresponding cipher-images with computational complexity of $O(L)$, where $L$ is the number of pixels in the plain-image. In contrast, the required condition in the previous deciphering method is eighty-seven pairs of chosen plain-images and the corresponding cipher-images with computational complexity of $O(2^{7}+L)$. In addition, three other security flaws existing in most Logistic-map-based ciphers are also reported.Comment: 10 pages, 2 figure

Chosen-plaintext attack of an image encryption scheme based on modified permutation-diffusion structure

Since the first appearance in Fridrich's design, the usage of permutation-diffusion structure for designing digital image cryptosystem has been receiving increasing research attention in the field of chaos-based cryptography. Recently, a novel chaotic Image Cipher using one round Modified Permutation-Diffusion pattern (ICMPD) was proposed. Unlike traditional permutation-diffusion structure, the permutation is operated on bit level instead of pixel level and the diffusion is operated on masked pixels, which are obtained by carrying out the classical affine cipher, instead of plain pixels in ICMPD. Following a \textit{divide-and-conquer strategy}, this paper reports that ICMPD can be compromised by a chosen-plaintext attack efficiently and the involved data complexity is linear to the size of the plain-image. Moreover, the relationship between the cryptographic kernel at the diffusion stage of ICMPD and modulo addition then XORing is explored thoroughly

The crossing number of locally twisted cubes

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory {\bf 59}, 145--161 (2008)] which solves the upper bound conjecture on the crossing number of $n$-dimensional hypercube proposed by Erd\H{o}s and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.Comment: 17 pages, 12 figure

Factorization of the Hückel Hamiltonian Matrix for Highly Symmetrical Molecules

A simple approach to the group-theoretical factorizing of the Hamiltonian matrix of highly symmetrical molecules is presented. This approach, which is based on the Lanczos method, requires only a symmetry-adapted linear combination (SALC) for each category of irreducible representation (IR) of the molecular point-group, while it reduces the size of the problem by more than one order of magnitude. We demonstrate the treatment by applying it to the study of electronic structures of the Goldberg type-II fullerenes, Cgo, C1go, C320, C50o and Cggo within the Hückel tight-binding framework. The results, in terms of the factor characteristic polynomial (or the subspectrum) for each category of irreducible representation, are presented for these giant molecules

Data mining for high performance compression of genmoic reads and sequences

University of Technology Sydney. Faculty of Engineering and Information Technology.The rapid development of next-generation sequencing (NGS) technologies has revolutionized almost all fields of genetics. However, the massive amount of genomic data produced by NGS presents great challenges to data storage, transmission and analysis. Among various NGS-related big data challenges, in this thesis, we focus on short reads data compression, assembled genome compression and maximal exact matches (MEMs) detection. First we propose a new compression algorithm for short reads data. The method utilizes minimizers to exploit the redundant information presented in reads. Specifically, large -minimizers are used to group reads and (, )-minimizers are used to search suffix-prefix overlap similarity between two contigs. Our experiments show that the proposed method achieves better compression ratio than the existing methods. Furthermore, we present a high-performance reference-based genome compression algorithm. It is based on a 2-bit encoding scheme and an advanced greedy-matching search on a global hash table. The compression ratio of our method is at least 1.9 times better than the best competing algorithm on its best case, and our compression speed is also at least 2.9 times faster. Finally we introduce a method to detect all MEMs from pairs of large genomes. The method conducts a fixed k-mer sampling on the query sequence and the index -mers are filtered from the reference sequence via a Bloom filter. Experiments on large genomes demonstrate that our method is at least 1.8 times faster than the best of the existing algorithms. Overall, this thesis work has developed efficient algorithms for pattern discovery from and for data compression of genomic sequences of big size